Chlorine occurs as a mixture of two isotopes, ^35 Cl and 37 Cl . What is the ratio of the diffus

step 1 So in this question, we're asked to find the relative rates of three different types of CL2. We'

Chlorine occurs as a mixture of two isotopes, ^35 Cl and 37...

Chlorine occurs as a mixture of two isotopes, $^{35} \mathrm{Cl}$ and 37 $\mathrm{Cl}$ . What is the ratio of the diffusion rates of the three species $\left(^{35} \mathrm{Cl}\right)_{2}, 3^{35} \mathrm{Cl}^{37} \mathrm{Cl},$ and $\left(^{37} \mathrm{Cl}\right)_{2}$

Key Concepts

Isotopic Variations and Molecular Mass

Isotopes of an element differ only in their neutron numbers, which results in small but significant differences in atomic mass. When these isotopes form molecules, such as diatomic chlorine in different isotopic combinations, the effective molecular mass changes slightly. This variation directly impacts physical properties like diffusion rates, as lighter molecules diffuse faster than heavier ones according to Graham's law.

Graham's Law of Effusion/Diffusion

This law states that the rate at which a gas diffuses (or effuses) is inversely proportional to the square root of its molecular mass. It is a key principle used to compare diffusion rates between gases of different molar masses, allowing one to predict how changes in mass, such as those due to isotopic differences, affect the speed at which molecules spread out in a medium.

Effective Molar Mass in Diatomic Molecules

For diatomic molecules composed of isotopes, the effective molar mass is calculated by summing the masses of the constituent atoms. The alteration in mass due to different isotopic combinations means that even subtle differences can lead to measurable variations in properties such as diffusion rates. Understanding how to compute and compare the effective molar masses is crucial when applying kinetic theory to predict the behavior of such molecular species.

Transcript

Please give Ace some feedback